A strapdown inertial navigation unit contains inertial sensors (gyros and accelerometers) fixed within an inertial measurement unit (IMU). Because the sensors are fixed to the IMU chassis (“strapped down”), the angular relationship of their input axes to chosen IMU axes is constant, so rotations and accelerations measured by the sensors can be used to compute equivalent rotations and accelerations along IMU axes. Typically the IMU is fixed to the body of a host vehicle to be navigated, such as an aircraft or land vehicle, but it can be a free-standing unit carried by an individual.
For the unit to navigate accurately, the IMU's initial attitude, that is the IMU's angular orientation with respect to some chosen navigation reference frame, must be determined through an alignment procedure. (By long tradition the procedure is called “alignment”, even if, as in most strapdown systems, there is no actual repositioning of the unit. For such systems the “alignment” or more properly “self-alignment” procedure involves only the collection and processing of data from the inertial sensors and other data supplied by the user or obtained from other sensors.)
Specifically, the alignment procedure determines the directions of the orthogonal axes of the IMU with respect to a selected navigation reference frame. An oft-used reference frame is defined by vectors that point north, east and down at the IMU's location. The angular relationship between the IMU axes and the navigation reference frame is defined by the values of a selected set of attitude parameters. Several such sets are in common use. But whatever set is selected, the purpose of the alignment procedure is to develop numeric values for the parameters that constitute that set. For subsequent inertial navigation to be accurate, these values must be determined accurately.
When heading of the vehicle is unspecified, the alignment procedure is executed in two phases. The first phase, coarse alignment, determines heading to within, say, a few degrees, after which the second phase, fine alignment, is started. Fine alignment further refines the heading error, and also solves for various inertial sensor errors. The two phases are necessary because of the limitations of alignment algorithms that approximate the equations that govern the inertial system with linearized forms; this includes Kalman filters and most other alignment algorithms. The underlying assumption for such algorithms is that, for the ranges of the errors being estimated, the governing equations of the inertial system are well approximated by a linearization about a known approximate solution. But this assumption is not justified for an unspecified heading; the actual heading can differ as much as 180 degrees from an assumed heading, and the governing equations involve sines and cosines of heading, which are far from linear over this wide range. For such large initial errors, the ignored non-linearities in the governing equations limit the accuracy of the coarse alignment algorithm, corrupting not only the estimate of heading but also the estimates of other quantities such as inertial sensor errors. The fine alignment algorithm, on the other hand, can separate a richer selection of alignment and inertial sensor errors, and can do it more accurately, but only when all the initial errors are sufficiently small. So coarse alignment is undertaken first, to reduce the errors to sizes that fine alignment can accommodate.
Both coarse alignment and fine alignment operate on inertial data supplied at regular intervals by the inertial sensors, and on “observation data” from some external source. As defined herein, input data comprises the inertial data and the observation data. Observation data may be measurements by one or more aiding sensors such as a GPS receiver, or can be information supplied by the user, such as the fact that the vehicle is stationary. A common alignment approach is to initialize the inertial navigation system with externally-supplied or default values for the navigation variables and allow it to navigate. The resulting navigation data are used to predict the data for an external observation; then these predicted observation data are compared with the actual observation data. A Kalman filter algorithm uses the differences in the observation data and estimates of the probability distributions of navigation errors to estimate the navigation errors; the error estimates are applied as corrections to the navigation data. The process is repeated at regular intervals.
Coarse alignment begins by determining the attitude with respect to the local level plane and using the outputs of accelerometers as they sense the effect of gravity. Because gravity is so much larger than the accelerometer errors, under stationary conditions an accurate determination is made quickly, typically in a few seconds. In contrast, the determination of heading requires that the rotation of the earth be sensed by gyros. Earth rate is larger than the gyro errors, but slow enough that typically it takes on the order of a minute to determine heading to within a few degrees. Finally, fine alignment takes a few minutes more to reduce the heading error to a small fraction of a degree and to accurately estimate other system errors, such as those for inertial sensors. In total, for vehicles stationary with respect to the earth, the complete alignment procedure can take several minutes. For situations in which alignment must be preformed with aiding data of lesser accuracy (e.g., airborne Doppler radar), or while the system is experiencing vigorous dynamics (e.g., aboard ship in heavy seas), accurate alignment can take significantly longer.
Many operators of vehicles with inertial navigators want to prepare their vehicles for takeoff within a very short time. In military, medical and law enforcement applications, the time spent sitting on the runway while the inertial navigation unit completes its alignment procedure is lost time that can be critical to the safety of soldiers and/or citizens.
For short alignment times, there is a trade-off between alignment time and alignment accuracy. Within limits, a longer alignment time leads to better alignment accuracy and therefore to improved accuracy in the subsequent navigation. How this trade is resolved depends on the application and in some applications on decisions made by the user. For example, in an urgent situation, a pilot may elect to cut alignment time short, and accept the resulting degradation in navigation accuracy. Any improvement that allows the same accuracy to be achieved in less alignment time may also provide improved accuracy with the same alignment time, or may provide some combination of improved alignment time and improved accuracy.